Calculating Slope and Rate of Change on Graphs

The video tutorial explains how to calculate the rate of change or slope of a line on a graph. It begins by introducing the concept and clarifying that rate of change and slope are synonymous. The tutorial then discusses non-proportional relationships and common mistakes when interpreting graphs. It provides a detailed example of calculating rate of change with units, such as miles per hour, and generalizes the method for graphs without specific units. Finally, it covers how to calculate negative slopes, emphasizing the rise over run method.

What is another term used for the rate of change of a line on a graph?

• Vertex

• Axis

• Intercept

• Gradient

Why is it incorrect to simply divide distance by time to find the rate of change in the given example?

• The time is not measured correctly.

• The relationship is not directly proportional.

• The graph is not linear.

• The distance is not in miles.

How do you calculate the rate of change when the starting point is not zero?

• Multiply the distance by the time.

• Subtract the initial value from the final value and divide by the time interval.

• Divide the total distance by total time.

• Add the initial and final values and divide by two.

What does 'rise over run' refer to in the context of a graph?

• The change in y-values divided by the change in x-values.

• The slope of the x-axis.

• The total distance traveled.

• The time taken to travel a certain distance.

In a graph without a story, how can you describe the steepness of a line?

• By determining the rise over run.

• By counting the number of points on the line.

• By measuring the length of the line.

• By calculating the area under the line.

If a line rises 4 units and runs 1 unit, what is the slope of the line?

• 2

• 1

• 4

• 3

What is the slope of a line if it goes down 1 unit and runs 3 units to the right?

• -3

• 1/3

• 3

• -1/3

How can you interpret a negative slope on a graph?

• The line is increasing as it moves to the right.

• The line is horizontal.

• The line is vertical.

• The line is decreasing as it moves to the right.

What does a slope of 4 indicate about a line on a graph?

• The line rises 4 units for every 1 unit it runs.

• The line is flat.

• The line is vertical.

• The line runs 4 units for every 1 unit it rises.

What is the general method to find the rate of change on a graph?

• Calculate the total area under the graph.

• Find the change in y divided by the change in x.

• Count the number of data points.

• Measure the length of the graph line.